Power-train controlling apparatus and method of controlling power train

A power-train controlling apparatus controls a power train of an engine electric hybrid vehicle. The power train is provided with an engine, a catalytic converter, an oxygen-level sensor, an engaging element, and an electric rotating machine. The power-train controlling apparatus includes a fuel injection controller, a catalyst diagnosing unit, and an engaging-element controller. The fuel injection controller stops fuel injection to the engine during coasting of the vehicle while the engaging element is engaged, introduces oxygen to the catalytic converter, and resumes the fuel injection in a fuel-rich state while the vehicle is running. The catalyst diagnosing unit diagnoses the catalytic converter after the resuming of the fuel injection. The engaging-element controller prohibits transition of the engaging element to a released state during a period between the stopping of the fuel injection and completion of the diagnosing of the catalytic converter.